Washington -LRB- CNN -RRB- -- Former FBI and CIA Director William Webster will lead an outside investigation of the FBI 's `` policies , practices and actions '' before the November massacre at Fort Hood , the bureau announced Tuesday .

Webster , a former federal judge , conducted a previous review of the FBI following the exposure of double agent Robert Hanssen in 2001 . He has been asked to look into `` whether there are improvements to our current practices or other authorities that could make us all safer in the future , '' current FBI Director Robert Mueller said in a statement Tuesday .

`` We must be sure that the systems we have in place give investigators the tools they need to carry out their responsibilities , '' Mueller said . `` At the same time , we must ensure constitutional protections and the confidence of the American public we serve . ''

The FBI has said that Maj. Nidal Hasan , the Army psychiatrist charged with killing 13 people and wounding dozens at the Fort Hood Army post , came to its attention as part of an unrelated terrorism probe in December 2008 . Agents found Hasan and the subject of that investigation -- identified as a radical cleric from Yemen who had once preached at a Virginia mosque Hasan attended -- had been in communication , but their exchanges `` raised no red flags '' that would have turned agents ' scrutiny on Hasan , senior investigative officials said in November .

Webster , 85 , led the FBI from 1978 until 1987 , when then-President Ronald Reagan named him CIA director . Webster took over the spy agency in the aftermath of the Iran-Contra scandal and led it until 1991 .

The FBI already has conducted a preliminary review of the Fort Hood matter . Meanwhile , the Pentagon is conducting its own investigation into whether any signs that could have warned of the rampage were missed .

Webster 's investigation will be coordinated with the Defense Department to avoid interference with the Army-led inquiry , and he `` will have complete access and whatever resources necessary to complete the task , '' Mueller said .

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FBI `` policies , practices and actions '' before Fort Hood massacre are under review

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William Webster , 85 , a former FBI and CIA director , will lead the investigation

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Webster led a probe of FBI practices after a notorious spy case in 2001

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Inquiry will focus on lack of `` red flags '' after suspect 's actions drew FBI attention